Charles Ramsey, the neighbor who said he helped free three women from a Cleveland house of horrors, told "Nightline" that another neighbor, Angel Cordero, got to Amanda Berry before him, then decided to walk away. But that is not how Cordero tells it.

"I helped her and I was first," Cordero told ABC's Cleveland affiliate WEWS-TV in Spanish."Ramsey arrived after she was outside with the girl. But the truth who arrived there, who crossed the street, who came and broke the door, it was me."

In an interview with "Nightline" anchor Cynthia McFadden, Ramsey, 43, described what he said happened Monday afternoon when he helped rescue Berry, Gina DeJesus and Michele Knight, who allegedly had been kidnapped by Ariel Castro.

Ramsey said he was sitting inside his home, eating McDonald's, when he heard a piercing scream from the house next door.

"[A] scream that is etched in my head forever," he said. "That sound stopped children from playing. Everybody looked at that house."

Ramsey said he first looked out of his window and saw his neighbor, Cordero, who Ramsey called, "the Dominican," run from across the street to alleged kidnapper Castro's house, which is next door to his. Then Ramsey said he raced outside to see what was going on.

"He ran over there, saw her, 'Please help get me out,'" Ramsey said, mimicking a woman's voice. "That's what made me go over there and say, 'Who the hell is trying to get out?'"

At first, Ramsey said, he thought someone had broken into Castro's house, gotten themselves locked in and couldn't escape. But that all changed when he saw Berry's face.

"When I saw that girl, I don't recognize her, I saw a white girl, [I said] 'What's your problem?'" Ramsey said. "Keep in mind, the Dominican, as I'm saying this, runs back over there behind me. I look across the street and say, 'She needs to get out of here.' He says, 'I'm not getting involved in that.'"

Ramsey said he then "did what I had to do" to get Berry out of the house. When the door wouldn't open, Ramsey said, he helped her bust out the aluminum bottom so she and her daughter, whom Ramsey said was with her, could break free. After Berry and the little girl were out, Ramsey said, he called 911.

"I took the phone and called 911, and I said [to Berry], 'Now listen, now you go across the street and you see that f*** that didn't help you, go get his cellphone. You call 911 from his phone. That way, while I'm trying to get through and you trying to get through, we both bound to make this happen,'" he said.

That's when Berry ran into a neighbor's house across the street and made the dramatic 911 call in which she said, "I'm Amanda Berry, I've been kidnapped and I've been missing for 10 years and I'm here I'm free now."

Cleveland Police Deputy Chief Ed Tomba singled out Ramsey by name in a news conference Wednesday, saying he deserved to be rewarded for responding to Berry's cries for help.

Since then, Ramsey has been hailed as a hero. Hodge's Cleveland, a downtown restaurant where Ramsey works as a "dish technician," started selling T-shirts with his likeness and the words "Cleveland Hero -- Charles Ramsey" on them.

The proceeds, according to the restaurant, will go to charity.

The restaurant's assistant general manager, Jimmy Henthorn, said Ramsey came into Hodge's the day after the amazing rescue.

"Chuck stopped in to get his paycheck, saw everyone, and just wanted to say, 'Still have my job, right?' And I said, 'Of course you still have your job.' He said he was looking forward to just getting back to work."

"He will be back for sure," said another co-worker, Peter Brooks. "All of us hope that he does."

But now, Angel Cordero is saying that he helped the women escape, not Ramsey.

Aurora Marti said she was the first person to see Amanda Berry screaming in Castro's doorway.

As Marti and her friend, Ana, crossed the street towards Berry, they called out to Ramsey for help, but with the women's broken English, communicating was hard, Marti told ABC News. So the women yelled for help from their friend, Angel Cordero, a fellow Spanish speaker.

Ramsey was there and did help free Berry, Marti said, but it was Cordero who kicked down Castro's door, setting Berry free.

When Berry screamed, "I'm Amanda Berry!" according to Marti, she replied, "No, Amanda Berry died years ago."

Cordero and Ana both agreed with Marti's version of events.

Neither Marti nor Cordero deny that Ramsey was there and that he helped, Marti said, but the heavy lifting to set the women free, according to Marti, was done by Cordero.